Model · compound growth · decide yourself
Same caret (^) as the Ham/Nye population catch: compound growth, not simple interest.
Start with one penny. Double it every day. That is v = 2^(d−1) cents on day d. Day 31 is not “31 pennies plus interest” — it is about $10.7 million.
Figure 1. Classic penny-doubled series · log-scaled bars so day 31 remains visible.
If a population model doubles every generation for 31 generations, headcount scales like 2^g. Generation 31 ≈ 2.15 billion in the pure doubling toy model. This is a potentiality sketch — not a claim that history was pure doubling with no death, famine, or migration.
Figure 2. Toy population doubling to generation 31 (log scale).
At 25 years/generation, 5,000,000 years ≈ 200,000 generations. A pure-doubling model across that span is not a sober demographic history — it is a reductio on treating deep time + continuous people as if growth were unconstrained compound interest. We show the scale; you decide what potentiality you accept.
Figure 3. Doublings needed for ~8B vs generations inside 5 Myr (log counts).
Bias stated: we lean toward God and responsible reading of math. We do not require flat-earth ideas. Potentiality ≠ proof. See also Ham/Nye caret note and Theorem G.
Defend Your Sins · biased toward God · responsible · no flat-earth theater · cite academics · decide yourself